1. Field of the Invention
The present invention relates to an electron beam writing method to be used in processes for manufacturing a semiconductor device and a liquid crystal display or a process for manufacturing a lithography mask to be utilized in the processes, and to a control for the dimension of a pattern to be written by an electron beam. 2. Description of the Related Art
For example, in a process for manufacturing a photomask, there has conventionally been used an electron beam writing method for writing a predetermined pattern by an electron beam for a resist film formed on a photomask blank.
In the electron beam writing method, a control for the dimension of a pattern to be written has a problem in that a dimensional error made by a proximity effect and a Foggy effect is to be compensated as described in Japanese OPI Patent JP2003-332203 and Japanese OPI Patent JP2003-107665.
The proximity effect represents a phenomenon in which a dimensional error is made by exposing a resist to a light with an electron beam (a backward scattering electron) transmitted through a resist film and reflected (scattered) from the surface of a substrate, and an influence range in the use of an electron beam of 50 kV is approximately 15 μm, for example.
The Foggy effect represents a phenomenon in which an electron scattered from the surface of a resist film or the surface of a substrate is reflected by a column or a chamber in a writing device and reaches the resist film again to expose the resist to a light, and has an influence within a range of approximately 30 mm depending on the structure of the writing device.
Referring to these two phenomena, the proximity effect represents a fog caused by the backward scattering of an electron beam transmitted through a resist film and the Foggy effect represents a fog caused by scattering through the column of a reflected electron on the surface of the resist film. Although both of them have an extreme difference in causes and scattering radii, they are fog phenomena. In both of them, the total energies of the electron beams generating the fogs are almost equal to each other.
Under the historical circumstances that the Foggy effect was found after the passage of a long time since the establishment of a proximity effect theory, however, the Foggy effect has been treated as a separate phenomenon from the proximity effect and the dimensional error of a writing pattern has also been corrected individually for each effect.
Conventionally, the dimensional error of a writing pattern which is made by the proximity effect has been corrected in the following manner.
A proximity effect correction (PEC) used in a general writing device utilizing an electron beam of 50 kV serves to compensate the influence of backward scattering by regulating a dose (an amount of exposure), thereby correcting a dimensional error as shown in FIG. 5. In a recent writing device, the amount of exposure is calculated by using a recalculating technique. In the recalculating technique, the same technique as a correcting method in a former generation writing device is used for a first calculation and a different equation is used in a second recalculation and thereafter. The newest writing device serves to carry out these calculations while performing exposure. For this reason, various techniques for simplifying the calculations have been employed in order to easily carry out a processing by means of a calculator.
However, the first calculation in the recalculating technique includes a special assumption that “a pattern density is constant for a calculating object and a periphery thereof”. Although the equation for correcting the proximity effect is very simple, that is, can be described in only an arithmetical operation, the first calculation includes the special assumption and has a leap in logic. For this reason, an excellent correction cannot be carried out.
[First Calculation]
The first calculation in the recalculating technique, that is, the correcting method in the former generation writing device is carried out in the following manner.
First of all, the degree of backward scattering is estimated. For example, the estimation of the backward scattering for a writing pattern E0 on a center in FIG. 5 is carried out by dividing the influence region of the backward scattering into cells having a predetermined size (0.5 μm square (in all directions) to 1.0 μm square (in all directions)). More specifically, the area of a writing pattern occupying the cell is obtained every cell. Assuming that the writing pattern occupying each cell is present on the center of the cell, the degree of the influence of the backward scattering from each cell to a cell on which the writing pattern E0 is written is weighted and multiplied to obtain a stored energy ratio Ebp for the backward scattering. In the case in which all of the cells are written including the cell in which the writing pattern E0 is written, Ebp is equal to 1. In this stage, the result of the proximity effect correction has not been calculated yet. For this reason, it is assumed that all the writing operations are carried out in the same dose. Ebp in the first calculation is represented as Ebp0.
FIG. 6 shows an energy profile in electron beam writing. Herein, a unit system is formed in such a manner that an amount of exposure generates a forward scattering energy. Moreover, a forward scattering energy profile is set to be a trapezoid in order to simplify a calculation, and backward scattering is represented as a perfectly flat offset. A width X0 of the inclined portion of the trapezoid representing the forward scattering is a parameter representing a resolution reflecting a beam profile, the forward scattering and the performance of a resist. The intersecting point of the inclined portion of the trapezoid and a developing threshold Eth indicates the position of the edge of a pattern to be written.
Referring to any writing pattern to which a dimension is to be adapted, next, description will be given to a method of adapting a dimension to an isolated pattern in the case in which the backward scattering is not present. In this case, the position of the edge of the writing pattern is represented as Xa and the amount of exposure at this time is represented as a reference dose Da.
The backward scattering is present so that the edge of the writing pattern is shifted to Xb (a state set before a correction). If the amount of exposure is changed from the reference dose Da to a correction dose Ds0, the position of the edge of the writing pattern is corrected to Xa (a state set after the correction).
The corrected dose Ds0 in a first calculation is expressed in the following [Equation 1] from the model, wherein the ratio of an energy absorbed by the forward scattering to an energy absorbed by the backward scattering is represented as ηe.Ds0=Da/{1+(Da/Eth)ηe Ebp}  (Equation 1)
In an actual writing device, it is assumed that the following [Equation 2] is established by the principle in which the diameter of an electron beam is coincident with the dimension of a writing pattern.Da/Eth=2  (Equation 2)
Consequently, Ds0 is expressed in the following [Equation 3].Ds0=Da/(1+2ηep Ebp)  (Equation 3)
Herein, the [Equation 2] is not always established in an actual process. For this reason, ηep in the [Equation 3] indicates a simple device control parameter.
As described above, the correction includes an assumption that “a pattern density is constant for a calculating object and a periphery thereof”. Although the backward scattering is represented as [Da·η·Ebp] before the correction, it is changed to [Ds·η·Ebp] after the correction. It is assumed that all of writing patterns E1, E2 and E3 in FIG. 5 are written by the same dose Ds.
Depending on the correcting method, an accurate correction is carried out for an L/S pattern in a wide area in which a pattern density is constant for a calculating object and a periphery thereof. In the case in which the pattern density is not constant for the calculating object and the periphery thereof, however, the accurate correction is not carried out. It is apparent that the correcting method is the product of a compromise to obtain a result which is moderately close to a correct answer by a minimum calculation in the days in which the resources of a calculator are insufficient.
[Recalculation]
Also in a recalculation, a stored energy ratio Ebp for the backward scattering is calculated. First of all, description will be given to a first recalculation. The recalculation does not use an assumption that all of a calculating object and a periphery thereof are written in the same amount of exposure. The stored energy ratio Ebp (Ebp1) of the backward scattering to be used in the first recalculation is calculated by using the amount of exposure to be the result of the first calculation.
In the recalculation, the amount of exposure on the periphery of the calculating object is not coincident with the amount of exposure of the calculating object as shown in FIG. 7. For this reason, a backward scattering offset is fixed and only the amount of exposure of the calculating object is regulated to carry out a correction.
A correcting equation guided from such a model is expressed in the following [Equation 4].Ds1=Da{1−(Da/Eth)ηe Ebp1}  (Equation 4)
For the same reason as the first calculation, the following [Equation 5] is used in an actual writing device.Ds1=Da(1−2ηep·Ebp1)  (Equation 5)
As a matter of course, when the amount of exposure is changed by the recalculation, actual backward scattering is also influenced. Referring to the influence, the recalculation is carried out plural times to converge on a correct value. More specifically, it is said that the recalculating method is a kind of feedback circuit.
After a second recalculation, a stored energy ratio Ebp of the backward scattering is obtained to repeat the same technique by setting, as an initial value, a value obtained by a last recalculation.
In the first calculation and the recalculation, the calculating equations are different from each other. The reason is that the magnitude of the backward scattering is not changed in the recalculation, and therefore, there is brought an over correcting state in which Ds is extremely small in some cases.
In the recalculation, if an initial value is excessively different, a convergence is delayed. For example, the recalculation is to be carried out ten times or more in order to obtain, through the execution of all of the recalculating equations, precision in which the recalculation is carried out almost twice by setting the result of a first calculation to be an initial value. More, specifically, it can be said that the first calculation is not always carried out on the correct assumption but precision in the initial value in the recalculation (after a second calculation) is sufficient.
[Correction of Foggy Effect]
For the correction of a fog by the Foggy effect, basically, a calculating mesh is expanded to approximately 1 mm, thereby carrying out the first calculation.
An actual dose is described in the following [Equation 6] for a reference dose, that is, a dose in which a writing pattern having a predetermined dimension is to be formed in the case in which neither the proximity effect nor the Foggy effect is produced.
                              [                      Actual            ⁢                                                  ⁢            dose                    ]                =                              [                          Reference              ⁢                                                          ⁢              dose                        ]                    ×                                                                 [                                  Amount                  ⁢                                                                          ⁢                  of                  ⁢                                                                          ⁢                  dose                  ⁢                                                                          ⁢                  modulation                  ⁢                                                                          ⁢                  of                  ⁢                                                                          ⁢                  proximity                  ⁢                                                                          ⁢                  effect                  ⁢                                                                          ⁢                  correction                                ]                            ×                                                                 [                                      Amount                    ⁢                                                                                  ⁢                    of                    ⁢                                                                                  ⁢                    dose                    ⁢                                                                                  ⁢                    modulation                    ⁢                                                                                  ⁢                    of                    ⁢                                                                                  ⁢                    Foggy                    ⁢                                                                                  ⁢                    effect                    ⁢                                                                                  ⁢                    correction                                    ]                                                                                        (                  Equation          ⁢                                          ⁢          6                )            
In the manufacture of a lithography mask such as a photomask, first of all, a pattern is written as described above on a resist layer coated to form a shielding film pattern on a photomask blank having a shielding film on a transparent substrate. Subsequently, the resist layer is developed to form a resist pattern and the shielding film is etched by using the resist pattern to be a mask, and the remaining resist pattern is peeled so that the photomask is manufactured.
In the electron beam writing method described above, there is the following problem.
More specifically, in a conventional electron beam writing method, the result of the proximity effect correction influences the Foggy effect, and furthermore, the result of the Foggy effect correction influences the proximity effect correction. However, such influences are not considered at all.
In the conventional electron beam writing method, moreover, an error made by the in-plane uniformity of etching or development cannot be corrected, and furthermore, a local loading effect caused by the etching cannot be corrected.
Furthermore, the amount of the proximity effect correction fluctuates in a plane so that the density dependency of a pattern dimension is changed in “a method of correcting a line width based on only an dose” as described in claim 13 of the JP2003-107665, for example.
With an increase in the integration of a semiconductor device, particularly, a mask pattern with high precision in a dimension is required in a lithography mask in which a pattern tends to be fine and complicated.